Carrier-current coupler



Sept. 16, 1952 B. E. LENEHAN 2,611,022

CARRIER-CURRENT coUPLER Filed Jan. ze, 1949 4 sheets-sheet 1 v I6 vn' Fig. I.

E v l 24 '45 I4 26 CARRIER TRANSMITTER l 2 f AND RECEIVER n n 27\ TL 'L .-I

24 22 -Xc=j/ WC ohms RL= 45o i so ohms W y' 'BERNARD E. LENEHAN. 72W.

BYQZ Z ATTORN EY Sept. 16, 1952 B, E, LENEHAN 2,611,022

' CARRIER-CURRENT CQUPLER Ns TuRNs N TURNS WITNESSES: g 8 INVENTOR www A BERNARD E. LENEHAN.

@ www A ATTORNEY Sept. E6, 1952 B. E. LENEHAN 2,611,022

CARRIER-CURRENT- coUPLER Filed Jan. 2e, 1949 4 sheets-sheet 4 n INVENTOR fr mi BERNARD E, LENEHAN.

ATTO R N EY .Patented Sept. 16, 1952 OFFICE CARRIER- CURRENT COUPLER BernardE. Lenehan, Bloomfield, N. J., assignor to- Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation of Pennsylvania Application' January 26, 194e, serial Ne. 72,894 s ciaims. (o1. 172-352) 1 f My invention relates to a coupling-device or network, for coupling the carrier-current from a power-line into a coaxial cable, andthence into the carrier-current transmitter-receiver set, or fOr COI-llllrlg the transmitter-receiver set, and the lead-in cable through which it delivers its output, to the coupling-capacitor which isl connected to the power-line. The power-line is usually a three-phase overhead transmission-line, using the term transmission-line in the power-engineers sense of transmitting electrical pow-er, at a commercial frequency such as 60 cycles, from one place to another place. The carrier-current is a superposed high-frequency current, usually in the frequency-range between 45 and 165 kilocycles (kc), vhich is vsuperimposed upon the power-currents for the purpose of intelligencetransmission over the power-line, for various purposes such as protective relaying, metering, remote control, and voice-communication. From the standpointof the communication (or highfrequency) engineer, the term transmission-line has a different meaning, which is always reserved exclusively for a network or a pair of'conductors in which the physical dimensions are comparable to the wavelength of the alternating-current owing therein, lor in which account mustbe taken of distributed capacitance or leakage. -.In this specification, the context may have to be relied uponjinsome instances', to determine the sense in which the expression transmission-line is used.

Previous to mypresent invention, in designing coupling-transformers or networks vof the class 'to which my invention relates, it has been ,the 'uniform practice to use a coupling-transformer [between the lead-in cable and the coupling-capacitor, and to provide the coupling-transformer with a large number of taps, on both its primary .and secondary sides, so that it can beA used as .a substantially'matched-impedance coupling between the lead-in cable 4and the power-line, at .any required carrier-,current frequency within the range of carrier-current frequencies over which the-*device is to be used. vIn matched-impedance couplings, the apparentjerminal im- `pedance which vis connected to ,theend of-the ,lead-in cable is equal to thev characteristic` impedance of the cable, whichis substantially a pure resistance, usually of a value ofthe order or" 50 or 60 ohms, in commonsizes and lengths of cables; and also the apparent terminal 'impedance which is connected to the power-line is substantially equal to the impulse-impedance of the power-line, which is substantially the characterstic impedance of the power-line from the standpoint of communicaticn-engineering, this impedance being usually of the order` of from 360 to 540 ohms, being commonly figured as either 450 or 500 ohms. When a communication-circuit transmission-line is terminated by a terminalimpedance which is equal to its characteristic impedance, vit operates vas iffit were an innitely long line, having no reflected, (or backwardlytraveling) wave.

The principal object of my present invention is to provide a muchV simpler coupling-'deviceI or network, in which, in general, mismatched impedances are provided, so that a single primary inductance and a single secondary inductance, with a knowncoupling-coecient betweenwthem, can be used acceptablyto serve a considerable range of carrier-current frequencies.

Heretofore, there were possibly -two reasons why a mismatched coupling-transformer was not previously designed' forcoupling the carrier-current lead-in cable to the power-line. One of these reasons may have been the failure to realize that the lead-in cable is fairly short, considerably less than one wavelength, as a result of which there is not enough time-delay in the cable to produce appreciable echoes or confused signals, if the impedance-mismatch is not too great.

vSince the cable is short, its power-losses are also relatively small, so that some increase inthese losses may well be tolerated, as a result of the mismatching of impedances. The other reason which undoubtedly would have militated against the design of a mismatched-impedance couplingtransformer has been the lack of formulas,V and the lack of precedent as to howtousez. such formulas as have been known, so that thecornmunication-engineer has not had readilyl available, (if indeed it could be considered to 'have been available at all), information as to the basis upon which such a transformer-design couldxbe undertaken or carried out. v More specically, it is an object of my invention t'o provide a coupling-transformer design, for coupling two communication-oircuitl transrnission-lines througha coupling-capacitor hav- Ving a capacitance C, so'that the coupling-transformer has Such secondary inductancelLethat "the total secondary-circuit impedance Vis somewhere near'zero (or resonance), or, in

usable. In other words, as will be subsequently explained in connection with Fig. 4, the operating-point is not to be at H, on the resistanceaxis OR, but at, or somewhere near, the point G, within the limits stated.

While I am not limited to a transformer having a constant or non-variable primary inductance Lp, another object of my invention may be stated to be to provide a coupling-transformer in which .a constant value of the primary inductance Lp and a constant value of the secondary inductance Le will be used over a range of frequencies, under mismatched impedance vconditions Which are chosen according t'o my invention so that, even in the center .of thefrequencyrange, the conditions will fnot inecessarily approach matched-impedance"-conditions. 'This mismatching of impedanceissuch -as to, produce a backward-to-forward standing-Wave voltageratio Es/Ei-=b, in the lead-in cable, whichsli'all but not more than 3.2 times (and,preferably.` not morethan 2.2 times)A said matched-rcouplingloss, or. notV more -fthan about 3:2V ydecibels .(db.) alto- Q'further objectV of .my invention'is to', provide a v uiu1vali-ngtransformer forjthe, purpose described, inwhich the value of the primary inductancelm is chosen-so as tti-adjust or; adapt. thecharacteristic cable-impedance Re, to the Powell-line Timpulse-impedance Rr., 011,. more accurately,':to.. ad-

just the characteristic,cable-impedance Rc1 tothe length of. the circle-diameterhaving fa value lcwyLs/RLV, Where; lcisr thecoupling-coeicient of the couplingtransfQrrnenand w=21rf isthefangu- 111-Y10Qty V@69611411.1113 upon .the .carriere'cu'rrent ff.r.ef1\1er1cyJ-Y Afstill further object -ofmy invention is tol provide'a 'coupling-transformer of "the class described, having aconstant'or-a substantially con- .-stan t, primary .inductance Ip, 'and Ihavi'ng .--a multiple-tap Aor variable" seconda-ry inductanceLs, the" number of secondary ftaps being relatively small, sothatA each tap' or.l terminal-of the sec- -ondary'windingisuices for operation overa ma- -teralrangex of freq'uencies;A saidY rangeA extending bothV above and' below the frequency fat which the vrnisrnatching ofimpedances is the'least.A i

"':With .the foregoing' and `other lobjects] in View, 4my invention consists 'in the 7 systems, circuits, combinations', str uctures,`"parts, 'and methods 'of `design and operation, hereinafterclaimed, and illstrate'din the accompanying drawing, vWherein Figure l' is a diagrammaticviewof'circuits and apparatus showing' my .inventiony inan illustrativeormnffembodiment.

Figs. 2 `and "3 are equivalent-circuit.diagrams which will be referredtc in the explanationiof `theflnvention,

*Figfl is'Y 'a1 vector-.diagram ofthe.' input-impedance Zi of'thecoupling-'networh in terms of the primary reactance wLpAv of.v the coupling-transthrough fa-.circuit-brealger I1. lrent:isf'substantiallyconfined to the one conducrshown inFig. 1,'not to scale,.and

Figs. 9 and 10 are vector-diagrams illustrative of the over-all performance of the coupling- .system .InFigure.1, I have indicated a block-diagram showing of "a carrier transmitter-and-receiver set .Egwhich is;connected to the input-end of a leadiin.coaxial-"cable` .'ILc, which serves as a communication-circuit transmission-line for enabling .thecarrier-setEto be housed in a building (not shown) which is close to, but not exactly underneath'ithe point where the carrier is to be coupled to one of the circuits of the commercial-frequency Athree-phase vtransmissiori-line or power-line TLL. -Theoutput-end of the lead-in cableTLc serves as Vthe Yinput-teijminal .I, 2` of .a coupling-network -which includesa lcoupling-transformer I4 and a -couplin g capacitor C. I 'Ihe upper terminal I5 of @the:coupling-capacitor C-is connected to one of ytheg conductors of the power-line TLL. Only one terminal of thepowerdine -TLLI is shown, this terminal :being-'connected toa station-bus I6 The carrier-curtcr, Qfethe transmissionline -TLL by means of a zcommonforrn ofcarr-,ier-current trap I8, which is connected in the, line-conductor between the CDEDlIlg-point |;5.,far1d thestation-bus I6 at the illustrated' terminal. of: the power-line TLi..

v4.In-the illustratedformfof embodiment of my invention, fasfshownfin 1, the coupling-capacitorj GaisA housed,l in `a known manner, in an :nsulatingfhousing@which is mounted on the .topfofrfa diagrammatically indicated box or base 2I which houses the-coupling-transformer I4 and certain other equipment, asv will now be described.

Theslower'terminalzz `of the coupling-capacitor C.is.:cpnnected. through a switch 23, to a terminal chend-tap ofthe secondary side of the coupling-'transformer I4. formerisishown, by 'way'oi giving a concrete il- 50` 4ingftheztwo terminals and 2, and an intermeidiate'primary-winding tap I, which is indicated,

This coupling-translustration, in Fig.l1; as an autotransformer, havin Fig. 1, as being adjustable, although, in gen- `er'aljthe primary-winding adjustment will not be :.neededat Aall,and,;if used at all, it will provide onlyia: small 'percentage-change in the number :ofprimaryl turns. 'The autotransformer-terminal Zis illustrated as .being-connected, through a con- ..d11ctor1.26; vtoa ground-Win21', which is grounded "asshownatl,

' Also included'in'athecoupling-capacitor base 2I,ithere"is usuallyprovided a 60-cycle by-pass `orJdrainacoilLI,'fwhich is connected between the lower Vcapacitorf-terminal?22 and the ground-lead :21,1thiSSdrain-coilbeing shunted also by a pro- -tectivei'gaplSZ- andla grounding switch 33.

Thecoupling-transformer I4, as indicated in Fig.' 1,-usua1lyfhas oneA or'more intermediate secondary-taps,which can be selected by the se- ".The.'equivalenti'carrier-current circuit for the apparatuslshwn in'Fig. 1, is diagramma-tically Aindicatedin"Figf'Z. "In'this figure, the carriervcurrentset E4 is fshownl simply as an alternating .,'sourceLE' This source would have a frequency of lector'-switch?23' .as-will be subsequently described.

it will he seen that the length of this cable is 1 short, when measured in terms of the carriercurrent wavelength. The length of the powerline TLL, however, is very long, when measured in terms ofthe carrier-current wavelength.

In Fig. 2, the self-impedance of the autotransformer I4 is divided into three parts, namely the primary impedance Zp of the portion of the transformer included between the terminals I and 2, a second partial-impedance portion Z2 which embraces the turns which are included between the terminals I and 24, and the over-al1 secondary impedance ZS which is the entire secondary impedance of the turns included between the two terminals 2 and 2d. The mutual inductance between the two portions Zp and Zz is indicated as Mp2, and the mutual inductance between the primary and secondary portions Zp and ZS is indicated as M. The over-all mutual impedance is therefore jwM=iwMpz+Zp ohms. The over-all secondary impedance is Zs=Zp+Z2+fi2wMp2 ohms. In this iigure, the reactance of the coupling-capacitor C is indicated as -Xc=-y`/wC ohms, the minus sign being indicated because it is a capacitive reactance rather than an induetive reactance.

In any practical case, we may assume that the primary and secondary resistances Lp and Ls of the coupling-transformer I4 are negligibly small as compared to the characteristic impedances or impulse-impedances Ro and RL of the lead-in cable TLc and the power-line TLL, respectively; or else the impulse-impedances may be considered as being (Rc-I-Rp) and (RH-RS) respectively. Neglecting the transformer-resistances, therefore, the equivalent circuit for Fig 2 is approximately as shown in Fig. 3.

,The input-impedance of the network is the equivalent network-impedance as seen when looking into'the'network at the input-terminals I, 2 in Fig. 3. It is,

- Let lc, a quantity less than unity, represent the coupling-coeiiicient between the prim-ary inductance-portion Lp and the complete secondary inductance Ls. Then Y f `Substituting this Value in Equation l, we iind the input-impedance of the network of Fig. 3 to be,

6, l whence the ratio of the input-impedance Z1 of the entire network to the'magnitude of the pri-i mary impedance wLpof the coupling-transformer This equation may be interpreted by Fig. 4, in which Va rectangular system of Cartesian coordinates is used to plot the resistance Rand the reactance iX of the impedance-ratio Zi/wLp. In this gure, the semicircle GI I P Q represents the locus of the end of the vector OP representing the impedance-ratio Zf/wLp, as the value of the uncanceled secondary-circuitA inductance i varies between a resCmance-condi'tionl at G, in which the frequency is such as to make the total secondary-circuit inductance (wLs-l/wCJ equal to zero, and an extremely high-frequency condition at Q, in which the value of the uncanceled secondary-circuit inductance (wle-47,00)` approaches (It will be understood that subresonance frequencies would produce the up p e r half of the circle GHPQ.) The vertical line OQ,

' with a length of one measurement-unit (to whatever scale Fig. 4 is drawn) represents tl term i in Equation 4, and the horizontal line QG, with a length of lczwLS/RL measurement-units, repreits the diameter of the circle GHPQ. The line OP represents the value of the impedance-ratio Zi/wLp at any higher-than-resonance frequency at which the uncanceled secondary-circuit inductance (wLs-l/wC) `has any assigned value. It is readilyeen, from r'g. fi, that the equation for the line OP is where qs: PQG.

Several things are readily seen from Equations 4 and 4a and Fig. 4; namely, that Equation 4a is thejame as Equation 4, that the length of the line OQ in Fig. 4 represents the value of the prie mary reactance wLe, which is taken as the meas; urement-unit for the iigure, that the line OP in Fig. 4 represents the value of the impedanceratio Zz/wLp, or the valueof Z1 if wLp=1 measurement-unit, and that 'cos qs ances is not' needed', because: the lead-,in cable is fairiytshort; considerably less than. one wavelength, so that there is not enough timedelay in this cable to. produce appreciable echoes or confused. signals if the impedance-mismatchl is not too great. Moreover, the lead-in cablelosses are small, so; thatsome increase in. these lossesmayrwell be tolerated', as. a; result. ofi a mismatchingofimpedances On the other hand, the power-line 'ILnisvery long, compared to the wavelength corresponding' tov the. carrier-frequency f', and hence.v the.-v attenuation of. the carrier-current in ,thef power-line TLLI is quite' large, so tl:1atthere` Will'befno; appreciable backward wave in the power-lineY Th1., and the carrier-current in the power-line TL Will be substantially only aV forwardv current-wave z', as shown in; Fig.. 3, even.Y though `there is I considerable n iisf matching,ofiimpedances@infthe=coupling-network. Anyy mismatchlgi of the loadmpedance Z1 whichterminates. the lead-in transmission-line or cable.l TLc, will result ina; reflected, or backwardly traveling,l standingewave, andy in a. certain ratio between thevoltage-magnitudes EB/EF, of, the backward and forward standing-waves: in theleadfin-cable.. This. ratio, EB/Er, will. always be less than unity. We. will-callit b. The currents accompanying.V these waves are v LBVz-#EB/(L-,Rd and Ir=EF/Rc. If 'the' cable is suiciently short, and ifv the total resultant currents and voltages at any given point inthe Vcablev are designated I and V, respectively, it maybe considered that the following relationships exist, as shown in Figs. 5 and 6:

Rar-l b2"- 2b cos' The equation for thelocus ofthe end of a vector which represents 'the impedance-ratio Aaeirgoze .Za/Rc for an unmatched-coupled cable TLC, having a reflected wave Esrhaving a magnitude bEF and leading EF by thefangle, as 0 is varied from 0 to 366, is obtainedl from Equation 5f. Itis,

which. is a. circle, asA shown. in. Fig. 7L having a;- center Rcv atl the point.

(E: lili?, X:

unity at the scale to whichFi'g. 'Tis plotted, this scale be'ng theV value .of the'pcharacteristic cableimpedance'Rc, as indicated in the figure.

If the center-displacement Ru is known, the corresponding value of the standing-wave voltage-ratio b is found by solving Equation 5l, whence Roll R0v+1 Ir the vector which. represents the apparent impedanceZa ofthe lead-in cableTLc, expressed in terms of the characteristic impedance Rc of said cable, terminates anywhere` on the circle RiPiRz in Fig. 7i, the. ratio between the backward-wave voltage EB and. the forward-wave voltage EF is equal. toA the value of. b for which said circle is drawn. If the end of this vector fallsianywhere outside of the` circle, said voltageratio ismore than the valueb for whichithecircle is drawn. If the end of. this. vector falls anywhere inside of the circle, the voltage-ratio is'. less than said value of b. If the vector terminates on the resistance-axis at the point Rc, where 'a ORC is the measurement-unit on which the circle rIi the ratio of the backward-wave voltage E to the forward-wave voltage Erhas any given value b, (which is necessarily less than unity), the cable-losses can readily be calculated or approximated in terms of the matched-impedance cable-loss and the standing-wave voltageratio E/Er=b. 'I'he ratio of the power which is transmitted in the backward direction, divide-d by the power which is transmitted in the forward direction, is EB2/Er2, or b2. The net transmitted power is the differencebetween the forwardly transmitted power and the backwardly transmitted power. Hence, in order to transmit one unit of power when there is a backwardly traveling standing-wave of a magnitude- EB=bEF, it is necessary to transmit 1/(1-b2) units of power by the forward wave Eryand b2/(1-b2) units of power by the backward wave EB. This makes the net power 1/(1-b2)-b2/(1b2), or unity. At the same time, the losses inthe cable are 1/(1-b2)ib2/(1-b2). or (1+b2)/(1b2) times (or Ro times) what the losses would have been if no reflection (or backward wave) had existed, that is, (1+b2)/(1b2) times (or Ro times) the cable-losses for unit-power transmission under matched-impedance conditions.

The Equation 5f or 5g, expressing the value of the impedance-ratio Za/Rc during unmatchedcoupling conditions when there is a reected wave EB in the cable, may be rewritten in terms of the circle-radius, p=2b/(1-b2), and the centerdisplacement Ro=(1+b2)/(1-b2.), in .Fig 7. From an inspection of this figure, it is evident that the apparent impedance Za of the lead-in cable Tlc is determinable from the equation (5g) 3L-Ruim cos 0-l-jp sin 6 whence, by a change of scale, that is, by multiplying both sides of the vequation by the scale-ratio Rc/wLp, we have i (5r) Zfp=wlp Rg+p cos @--jp sin 0) :RH-p (cos -l-j sin 0) where Ra and p have the values stated in Equations -EZ and m, respectively, and the standingwave angle 0, defined in Equation 5a, may have any value from 0 to 360, depending upon the RcRo (5s) it-v wLp and its radius is Y Rop At the receiving (or power-delivering) end of the lead-in cable TLC, that is, at the input-terminals l, 2 of the coupling-networkin FigrS, the

output-voltage and current of the cable are idenl tical to the input-voltage and current of the network, so that, at this particular point,.the Vapparent impedance Za of the cable, as denedin Equations 5f, 5g, .5q and 5r', is always the same. as

the input-impedance-Zi of the network, as defined Y l i ic that the mst-named circle is drawn for the proper' value of the standing-wave voltage-ratio impedance RL, the coupling-capacitance C, and

the range of values of the angular-velocity w=21rf- Two coupling-transformer constants are to be determined, namely the primary inductance Lp, and k2 times the secondary inductance Le, where lc is the coupling-coefficient as dei-med in Equation 2. The transformer will have to have its highest secondary inductance Ls when the carrier-frequency (and hence w) is a minimum, and hence the transformer will have to be designed to have enough secondary turns to satisfy the required conditions when w is a minimum, or wmin; and then one or more intermediate tappoints (if necessary) may be provided for satisfying the operating-conditions for larger angular velocities w.

A little reflection will also show, (and my invention is alsopredicated on this), that the designer will also know that, if the maximumnumber of secondary turns, or the maximum secondary inductance Ls4 max, is to suiiice for a certain frequency-range vincluding other frequencies which are larger than the minimum carrier-frequency fmin, the uncanceledor effective total secondary-circuit inductance (wLs mx-l/wC) will become more inductive, and less capacitive, as the frequency increases.` Hence, as the frequency increases, the operating-conditions will change from a resonance-condition (such as the point G in Fig. 4) wherein wmln2CLs max 1 to a higher-than resonance condition (such as the pointP in Fig. ll) wherein v (6G) ZUgLs max 1 Or the secondary-circuit conditions may even change from a sub-resonance condition (corresponding to a point in the upper half of the circle, above the point G) wherein to a resonance-condition l(at or even to a super-resonance condition (at P in Fig. 4). In some few cases, the total uncanceled secondary-circuit inductance (wLemsxf l/uiC) may start with a super-resonance condition, in which the operatingpointV P will -be below `the point G in Fig- 4, but generally not enoughbelow G- to be as low as the pure-resistance axis OR in Fig. 4, and in this case,

(6C) y LUniinC-Ls max `1" Y l and the operating-condition wil-lcha'nge, in-

creasing angular velocities w, to an operatingcondition which is still higher than resonance (still further below the point G on the circle in Fig-.4).

y For aninitial design-assumption in Showingfthe design-calculations for a rst exemplary form -of my present invention, I will assume, by way of illustration, that the operating-point P 4in Fig. 4, at the minimum frequency and the maximum secondary inductance, is above the point .G -in Fig. 4, and specifically that it satisfles (for example) Equation 6b. This xes the value of the full-turn ('or maximum) secondary inductancelamx `of the transformer, as will be subsequently explained.

The designer may next consider the range of desirable values of the standing-wave voltageratio E/Er=b, and its effect upon the size and the displacement of -the 'rescaled minimum-frequency unmatched-coupling circle which represents all possible values of Athe cable-impedance ratio Za/WmmLp in Equation r. The maximum tolerable value of the reected wave, -EB=bE`F, during unmatched-impedance operation, is controlled' by :the amount of cablelosses which are to be accepted.

vI have already shown, in the discussion following- Equation 5p, that the cable-losses, with unmatched coupling, are Ro times the cable-losses with matched-impedance coupling, where R0 is The input-power which is delivered by the car- I rier-current source E to the cable-impedance Rc in Fig. 3 is where a is the attenuation-constant, and e is the base of the naperian logarithms.

The Apower-ratio-is which reduces to P.-/P0=e2a when 5:0, that is, for matched-impedance couplingwhen there is no reflected Wave E1s=bEr-A Equation 7b shows that the power-loss in the cable, when there is no reflected wave EB, that is, when b=0, is a nepers, or 8.686 a decibels.

When there is a reflected Wave of a magnitude l 2a 2--411 (7a) P. RC- e (l .be )RC EB =bE1v Equation 7b shows that the loss in the Most lead-in cables, such as TLC, for carrier-v current use, haveY a loss which is never more than 1 decibel during any conditions of matchedimpedance operation. If we make the pessimistic v 12 "assumption, 'therefore'. that the loss in the cable -is 1 decibel, with matched-impedance'coupling to -thepower--line TLD, thatis, with 11:0, Equation 'Ib-shows that this assumption means that and: Y Y

(sa) .aman-01105310 "Then, when there is. a reflected wave Ea=bEF, the power-ratio the cable; as expressed 1n Equation 7b, becomesy (SI1-l' gael-25899*02631125.92580.7944112 P1 lf-b2 1452" -db loss. 3.1111105 whence; (ser.) R11-P12589 11111011 Fig. 'n

E D 15111 m b IV-l-bz V b ,0. 1.2.59 .1 .1 1 0 0.25 1.200 1.1055 .e' 1.133 .533' 0. 5 1. 414 1. 5037 333 1. 667 1. 333 0. 54 1. 450 1. 6141 299 1. 823 1. 525 0. 55 1.100 1. e446 200 1. 810 1. 511 0` 56 1, $71 1. 6766 282 1. 914 l. 632 0. 57 1. 182 1 7098 2741 i. 963 1. 682 0. 5s 1. 404 1. 7447 200 2.014 1. 11s 0. 59 1, 507 1. .7811 258 2. 068 1. 810 0. 6 1. 520 1.8189 25` 2. 125 1. 875 0. 7 1. 705 2. 3175 176 2. 922 2. 745 0-8. j 2.085 3.71905.- 111 a. 556 4. 444 0:9 e 3.239 5."104 053' 0. 526 9. 474 0.19.5 5.16.50: 1.145 19. Y t19. 4e' .L i 'w 0 .w

Table -I sho. s that, V`as the. voltage-ratio EB/E1=b increases, (asa result of a progressive departure frommatched-irnpedancel coupling), the watts-loss -in the cablevbecomesa larger and larger number of times the matched-coupling value of this loss, asshown by column IV which lists the loss-ratio R0.y In `terms of decibels, as shown in column II, the increased loss is not very high, so that, if the matched-coupling lossA is less than 1 decibel (db).', the unmatched-coupling loss will be less than `l'. 5db when E11/EF is 0.5, less than 1.8 db when E1s/EF is 0.6, and less than '3'.21dbzwhen"ElErisias'high asno-.8. All' of these decibeli-lo'ssesi are, vin general, quite acceptable, particularly rangvbetween. 1.5 and 1.8' decibels',v or. 'iowen Table' I also shOWS'thaLt. as the standing-wave voltage-ratio 'Ea/Erz?) increases; (as a result of a-p'rogressivel departureffrom.matched-impedance coupling),A theucircle in.-Fig'. '1 comes closer and V"closexto thereactanceeaxis (as shown by' the decreasing values ofthe intercept' R1), and at 'the 'same tirnefit changes its shape, because the radius p fof thecircIe becomeslarger and larger.

4.In .order vto determinef the effect of the-standing-wave voltage-ratio E1s/EF upon the transi3.V former-design for' a given ratio b at any given frequency such as fmm, it is to be noted that this Fig.Y 7 Icircle (when redrawn to a scale which is Rc/wminLp times the Fig. 7 scale), determines the operating-condition of the coupling-network, by intersecting with the circle which is shown in Fig. 4. Since the redrawn and rescaled Fig. 7 circle, plotting Za/wmmLp, becomes flatter and flatter, that is, has larger and larger radii, with increasing=valuesof b, while at the same time approaching closer andl closer to the reactanceaxis, it is obvious that, with increasing values of b, if the Fig. 4 operating-point Pis to be kept on this circle, the scale-multiplying ratio Rc/wminLp will have to be simultaneously increased-that is, the primary reactance Lp will have to be simultaneously decreased. Hence` the transformerratio Lamu/Lp will have to be increased, simultaneously with the increasing values of the standing-wave voltage-ratio VI9=E`1s/Er, in order to cause the (rescaled) Fig. 7 circle to intersect the Fig. 4 circle at some desired operating-point, such as somewhere near the resonance-point G on Fig. 4, which is somewhere near the desirable minimum-frequency operating-point, as explained in connection with Equations 6 to 6c.

As a result of these considerations, the designer will first nx the maximum standing-wave voltage-ratio E/Erzb which is to be deemed acceptable at the lower end of the frequency-range i4 or a little more. or alittle less', cr anywhere in between these values.

` ,Equation ,9 .thus determines the value of the which is to be served by the highest-turn tap 24 Y on the secondarywinding Ls of the couplingtransformer I4. In general, b may be anywhere between 0.5 land 0.6, or b may even have a material value (not zero) which is below 0.5, or b may even, at times, have a value which is somewhat above-0.6, depending upon theextra decibellosses which are to be accepted, not only in the cablefI'Lc, but also in the coupling-transformer 4. 'Ihis determines the dimensions of the Fig. 7 circle, particularly the values of the center-displacement Ro:(1|b2)./(lb2) Vand the radius 19:21)/ (1-122), as computed in Table I.

As previously mentioned, in connection with Equations 6 to 6c, the designer will also have to make a preliminary guess or estimate as to the position of the minimum-frequency operatingpoint P on the Fig. 4 circle. In other words, the initial value' of the angle in Fig. 4 will have to 'be estimated. This angle is determined by the maximum (cr-full-turns) value of the secondary Y inductance Ls max. It l/wmln Cwmiu Ls max.)

-1 qs tan RL As has already been pointed out, in connection with Equations 6 to 6c, this angle qa should be f somewhere near zero; say

i 'i tan-uoicmwn mai/RL When N:tanV1(0) 20, we lhave the condition for resonance in the secondary circuit of the transformer le. It is to be understood, however, that the angle p may depart from the zero value,

4either Vabove or below the circle-diameter in Fig. 4. In general, in theimore conservative designs, the; value of the maximumsecondary vinductarice.wmmLsA 'max' should be so chosen, with maximums'econdary inductance, and that, in turn, determines the value of the Fig.' 4 angle. which is counting c positive when measured above the diameter shown at cef RL, t

It is best, at Athis pointVfcr .the designer to lmake a preliminary guess, or estimataas to the probable value ofthe.'coupling-coefficient lc of the particular kind of transformer which he has in mind, based upon his experience in designing that kind of transformer. This tentatively fixes the length of the circle-diameter in Fig. 4, according to Equation 9b. Then, after the transformer has been completely calculated, if the nal results do not agree with the assumed value of lc, this value will have to be corrected, and the calculations will have to be computed again, until the desired degree of accuracy is obtained. In general, a high degree of accuracy is not necessary. y

The co--ordinatesv 0f the operating-point P in Fig. 4 are apparent from the flgure,and also from Equation 4a. These co-ordinates are,

If. a graphicl solution is to be sought; the .designer will next want toplot Equation .5r onthe same drawing which shows the operating-point P Shaving the `co-ordinates (RP, XP). To this end, thek designer willhave to;- redraw Fig. 7 for whatever value of b he has chosen, (Fig. 7 was drawn ,for b:0.5); and the Vdesigner, will also have to rescale Fig. 7 in the scale-ratio Rc/wminLp, (so as to plot Za/wmmLp, as in Fig. 4 remembering thatZz=Za at the cable-terminal |,2).

" If...the operating-point` P, having the coordinates (R'P, XP);A is to lie on this redrawn and .rescaled Fig. .7 circle, representing Equation 5r,

thedistance of the operatingpoint P from .the circle-center R0', Equation 5s, will have to lhe equal to the circle-radiusp'f, .Equation 5t: thus,

y`From `Equation 9a. Awe maydetermine theprimary'inductance which is necessary tot the re- ,drawnand'rescaled Fig. 7 circle, for unmatched- 1'5 coupling conditions, that isffor nany-zgivenstanding-wave voltage-ratio rb, Iso th'at :this redrawn 'and rescaled circle will pass lthrough any ".par- .ticu'lar operating-point?, having the .co-ordinates (RP, XP). This value of the primary inductance If theprimary .inductance Lp ris rknown,` (or is to be varied), Equation 9g 'can' Abe rearranged to vshow the circle-center displacement Rn lof the 'original Fig. -7 circlewhich is 'required to make the rescaled circle of Equation f?" pass through the point"(Re;Xe). Thus,

, wsa-muws.www (91') Ro- ZRCRPUminLp Equation-9h determinesv the values of the two primary 'inductanoes Lp, either one of which will produce the given standing-wave Vvoltage-'ratio b, provided that RP, XP and Rc are known. l

From Equation 9h, since the quantityrunder the radical may not be negative, it is evident, in practicing my invention, `that 2 R02 r (5g-glitt@ qs) +1 the last substitution being made from Equation 9d. Equation 9j states that'the initial (or minimum-frequency) operating-point P in Fig. 4 may not .be made too high, `consid'efra'ticm of the loss-multiplying ra'tio Ro, vwhich isv also ithe circle-center .displacement-...in Fig. "1'; 4anclzn'eithcr can the center-displacementm fbe made too small, in lcons'idn'ation fof tan :as 'defined in .Equation 4b or 44b.

The foregoing equations .and desgn-pmcedures are perfectly general, applicable: to both ironcore and air-'core transformers, of' whatever vvalues of coupling-coefficients k. If the transformer is an iron-'core transformer,A lit must have extremely thin laminati-ons for theV 'core'. or else a powdered core, in accordance with usual high-frequency practice.

By way of illustration, I will apply these design-principles to the design of a 'concentriccoil air-core transformer, which is a Aconvenient type of coupling-transformer, the top half 'of which ,is shown in diagrammatic vsection (but .not to scale) in Fig. '8. It may be either a twowinding transformer or ranrautotransformer. -It is illustrated .in Fig. 8', (as well 'as 'in the equivalent-circuit diagram of Fig. 2) as an autotransformer, consisting of aninner coil orwinding, designated by the same reference-character as its self-inductance Lp, surrounded by an outer vor overlying coil or winding', designated by the same reference-character as its self-inductance L2. The .mutual inductance between these two windings Pp and L2 isl-d'esignated Mp2. The inner winding Lp constitutes the primary turns 11., which are also a part of the secondary turns `N='1'1.|'N, while the outer winding L2 constitutes theremainder, -N, ofthe secondary turns Nn The winding-turns Ns=n+N are wound in suc- 156 fcessive layers 40, wound oneon top of eachother. the inner layer being wound on a 'cylindrical insulating-mandrel 39. The 'overall mutual induct'an'ce between .the ,primary turns Np 4and the 'secondary turns .Ns is .designated 'by M.. and has .a value equal to (1'0) Ylll=1il1srilp This coupling-transformer Lp, L; must withstand lightning-surges up to the value ofi the protective gap 32 in Fig. .-1, which Vis yusuailyunder .15 'or 20 kilovoltsj. Hence, .-1 use `an additional layer 'of sheet-insulation INS.. which (for example) may be an acetate sheet having a thick- .ness of .005' inch, between successive layers 40 of the winding Lp, L2, in addition to the usual wire- .insulation INSw. This layerinsulation INSS .preferably extends Vsome vinch axially beyond each end of the winding Lp, La, .in order to obtain a vhigh creepage-'distance* insulation, as shown .in Fig. 8. This necessity vfor .protecting against lightning-damage results in a. transformer having a slightly larger coil-size, and hence a .lower coupling-coefcient Ic, than would :otherwise be desirable. .Y

-Let us ,-assumethat the yinner coil or 1primary winding Lp has n turns, and has 'a -mean radius a, an axial length rc, 'and a radial depth t, in inches, as shown in Fig. 8. -Let us assume that thevfouterA 'coil or exclusively secondary portion L2 has 'N turns, and has a mean .radius A, (say.) thej same -axial length z, anda radial depth '2, .infinches, as also lshown -in Fig. 8. Let us designate `the mean radius vof the complete secondary winding Lp, Ls, constituting all of the turns .Ns,=11;iN.as As, as indica-tedvin Fig. 8.

The approximatervalues of the self-inductvarices -of these'coils, using Formula 56 4on page l(i2-of 'Termans Radio Engineersr Handbook, are

The va'rfnpr'oXirnat'e value of the coupling-coei'cent 19152 between 'the two coils Lp and L2, using Termans formula 87 on pagel, is

a2 (10d) @2:25a

Two illustrative design-calculations will sufce. As a first example, let us determine the designconstants for a coupling-transformer for coupling carrier-current of a .frequency between 45 and kilocycles (kc), through a .004 microfarad coupling-capacitor C which is about as large as any4 that would normally be encountered iin-practice.A v

`llnis,letus assume: i l mi' F- l fm1n=45,`0'00"'cycles per second="minimum frequency fmax=165,000 cycles per sec0nd=maximum frequency `wmm==27f 15,000=.28274. 106 radians per second :winaX- Lzfrx165;000=1.0367 106 radians per second i RCL-:50' ohm'sy RL=450 Ohms C=.004 106 farad 1c=.8, 7c2=.64, when Ls is a maximum.

If We assume a sub-resonance condition at plus 'sign indicating that the anglelis measured vustofcalculate the required primar Lp from Equation 9h. Thus 45 kc., sothat some equation such as 6b', for example, is satiSed, then, with that assumption, the maximum (or full-turn) secondary induct- From Equation 4b or Equation 9a.,.the angle p in Fig. 4 is wmin L.: max

ates that the angle 'kPQG-p is Ameasured above the,v diameter (HQE,

which agrees with our assumption o'f'a sub-resonancecondition, with thef .frequency Lnotyhi'gh enough tof. make the secondary inductance wmixms` max, numerically equal` to the couplingcapacitance l/wminC. Y

The Fig. 4 circle would have to beredrawn, therefore, to satisfy Equations`4b and '9a' for a minimum frequency and maximumV secondary on the vertical (or reacta'nce).v axis, ,and .the horizontaldiameterl would be measuredoff to be above the diameter QG.) l g .r

The co-ordinates of the operating-point P in this redrawn Fig. 4 would be. determinedr by Equations 9c, namelyy Let us now assume, by:Y Way of giving a concrete illustration, that we'. can accept a possible maximum decibel-loss of 1.67 in the cable. Ref- "erence to Table I, or use of Equations 8b, Bc, and 5l,` shows that a loss of 1.67 'decibels corresponds t'o a' standing-wave voltage-ratio :of approximately b=0.56,1'and"a Fig.' 7 .center-displacement `of approximately R=1.91: This enables y inductance quired transformer-as having a coupling-coeffi-` cient k=0.8, an overall secondary inductancei' These` conditions can beusatised in trasformers of al'variety :of dierent lengths, radii, coil-thicknesses, and core-materials.'4 A Using- Mie type of transformer shown in Fig. 8, andchoosing a mandrel 39 of a convenient outer diamet'er, "of" say '1.875--inches, 'we1n1ig'li`t, as a rst trial, try using eight layers l0, each layer' containing 30 .turnsof No. 20 dcc.. wire, having a wire-diameter which' we 'will'assume 'to 'be .032 inch bare, plus wire-insulation INSvV 'having a thickness which, wewill assume-to be. .r005.inch. making a totalV outside wire-diameter of ,042 inch. Let us further try making the inner-'coil LpconsistV of 2 complete layers, while tllejouter coil Lz consists of 6 complete layers, using whole numbers yof layers for convenience in v`bringing out the taps and maintaining the insulation. Then, ifA the sheet-insulation INSS between successi'velaye'rs- 40 has afthickne'ss'of .005' inch, as assumed in Fig. 8, we willhave the ,following transformer-dimensionstld p l (llf) transformer, as determined by Equation 2 Equations. 10` to.A 10d, are as follows:

' :It win be' iit'ed that the' actuar'prmar ductance, Lp= 10*6, agrees reasonablywll with the value, Lpll'YXlOv-lwhich was calculated in Equation 11e; and that theactualio'verall secondary inductance,-Ls.v=2690 A10-", agrees reasonably Well with the value,

` rss-.emmer which was calculated in Equation lla; While the actual vcoupling-c'oeicient, lc .7994, agrees-'sumciently closely with the .originally assumed value, ulc- -.8,inEquation"ll, so that arecalculation is .f'E'or' thisv transfrmeras" -dened Ecfuation l 11g, and for the initially assumed system-constants as stated in Equation. 11,

(ebf') l 101,. CL.=.079943 '.o04 2`690=0.86o2

I the' angle PQG is 1.008-l-l.628). 282742)( 1552-!- 5()2 2 50X1.004 .28274 155 the standing-wave 4voltage-ratio is better than the originally assumed value, lar-0.56, being actually thedecibel-loss is 1 0 login (1.426) :1.54, the first intercept in Fig. 7 is' While-.the radius of said circle 42 in Fig. A'9 is QJ- 0 v wm L11-1.151112 v 1.141 1.sa1.995 The co-ordinates of the operating-point P in Fig. 9 are (1.004, 1.276), as given in Equation 11d'. -If we use the same transformer, wth'the's'ame nuo "kry-03994, and b=0.5142.

C20 .numbers of primary and secondary turns. and if we now --apply .some other carrier-frequency Jz=wz/21r, the diameter QG: of the new circle In in Fig. 9 becomes while the angle PzQGa' becomes ll (1lb qszstand(1.9649 f ,2 1.690213) f2 fmin and the co-ordinates of the new operating-point Pz become min.

fm in If We assume that, when we change the frequency from fmin to fz, the value of the standingwave voltage ratio .remains unchanged at b=0.5142, as found in Equation 5p,vthen Equation 5l will be controlling, in determining the value of the Fig. 7 center-displacement Ro, and Equation 9i will not apply, because the new rescaled Fig. 9 circle 422 no longer (in general) passes through the new 'operating-point (Rpg, Xen). Equation 5l shows that, if the voltageratio b is' constant, the Fig. 7 center-displacement Ro remains constant, independent of the frequency j or the angular velocity w=21rf, and hence, when We change to a new frequency f2 Without changing the backward-to-forward voltage-ratio b=Es/Er, the Fig. 7 center-displacement R remains constant at Ro=l.7l9, as determined in Equation 9i. 'Ihe new Fig. 9 circle v422, however, changes, because the scale-.ratio Rc/wzLp changes when the angular velocity changes from wmin to wz, so'thatthis new Fig. 9 circle 422 will now have a center-displacement Ruz:

and a radius pelamnsnaant 2 wzLp f2 fz The distance between the new cperatngmont P2 and the new circle-center R02' at any frequency f2 s I If the losses are to be kept as low as at the minimum frequency 1min, the distance PzRaz' of Equation 11h must not be greater than the circle-radius pz' of Equation 5t, at each value ofthe frequency fz. This problem can best be solved empirically or graphically, as Vshown in Table II, which shows the following data for each of a plurality of different assumed frequencies f2; namely, the input-impedance circle-diameter QG; of the circle 4in in Fig. 9 according to Equation 11e", the angle cz according to Equation 11b, the coordinates (Rpz, Xpz) of the operating-point Pz according to Equation 11d", the center-displacement Roz'- of the Fig. 9 apparentimpedance circle 422 according to Equation 5s", and the radius p2 of the Fig. 9 circle 422 according to Equation 5t", using the proper values of the angular velocity w. These quantities are calculated for the conditions, A.Rc-:50, RL=450,

' `TABLE II (FOI Flg. 9)

fz QG: du R Pz XP: Roz PzRhz P'z 'It should be remembered that thie'rabie n liscomputed for a standing-wave voltage ratio of En/EF.-b=0.5142, corresponding to a vmaximum possiblecable-loss of 1.54 db, assuming that the cable-loss under matched-coupling4 conditions would never be overA 1 db. When any operatingpoint Pz is on the unmatched-coupling circle 422 for that frequency, the'decibel-loss and the stand- 'ing'lwave voltage-ratio by have ltheir assumed values of 1.54 and 0.514, respectively. Whenlthe .operating-point P2 isinside of the corresponding circle 422, the decibel-loss and-the voltage-ratio'b vhave values which are smaller than the lvalues for which that ,circle 4h22 was drawn. When the j distance of the operating-point P2 from the center Roz of the unmatched-coupling circle `422 inFig.

9, iscqual-to the circle-radiusp'z, the operatingpoint P2 is obviously on the circle, and when'this distance PzRoz is smaller than .the radius pf2, the operating-point Rz is obviously inside of the circle.

' A comparison of the last two columnsof `"I "abl'e 1I thus shows that the backward-to-forward voltage-ratio EB/EF--b has its assumed value of 0.514

',when the carrier-frequency Iis-either,l.4x5l kilo,- cycles or 75kilocycles; this b-ratio ,is lessthan 0.514 at intermediate frequencies; and it is higher -than 0.514 when the frequency isless tllanffltl` or more than '75*kilocycles.

To avoid excessive confusion in Fig. 9,' the two circles 412 and 422 are drawn for only one addi. Vtional frequency, namely 60 kilocyclesin addi- .tion to the initial circles 4I and 42 for ,the minlmum frequency of kilocyclesfltis noted that,

as the frequency j increases, the circle4lrepre -senting the network-impedancel Z1 in terms of the primary reactance wLp, will increase insize having a diameter 13- equal to IcZwLe/Rr; whereas .the other circle, 42, representingtheapparent 'cable-impedance Ze in terms-of the primary ireactance wLp, will 'decreasein si'zeg'having` a radius f lp':ZURc/LUL'pG'-bz), and atenta-'displacement To find a smaller-turn secondary-tap 43 which 4will have a frequency-range overlapping, or nearly overlapping, the frequency-range for this maximum-turn tap, several procedures are available. For example, we might make the lower end of the frequency-range for the proposed tap 43 h-ave a value of kilocycles, so that there would be a iiD-kilocycle overlap of the two frequency-ranges,

one ending at 75 kilocycles, and the other starting at 65 kilocycles. (This is an arbitrary as sumption, as the frequency-"overlap may be anything reasonable, or it may even be zere.) n

We will then treat the-problem as a new transformer-design, starting out with the premise that the operating-point P in the Fig. 4 circle should be somewhere near the endGr of the horizontal diameter QG. For example, in Equations :6" to 6`c. or in Equation 9, we'might arbitrarily assume vthat (93) w3 mlnzLsSC 1 very roughly, where we min is the frequency of the tap-43 frequency-ranga'and Le: is the needed value of the over-all secondary inductance when the tap 43 is used. We have tentatively assumed that y wa m1n=21r 65,'000=0.4084 106 l Sometimes, several trials will be needed-,ztodetermine a suitable value of we min and a suitable approximation to unity in Equation 9 or 93, so as to. be" abletofplace the secondary tap 143 at the endof .oneof the secondary layers 40 (for con `venien'ce indesign and insulation, and so as to obtain a suitable upper limit, wa mex, of the 1fren-- quency-range for this tap 43) i Thus, in Equation 93, if we put l w3mm:0.4084 X 10*6 and .A v

v -'C=0.0()4 106 as in Equationlll, we findthat .thevsecondary inductance Les, when usingv thegtap v43, shouldbe roughly about 1500 10`-6 henrys. We h aveealready found that the full-turn secondary terminal, using all eight secondary layers 40,- gave a secondary inductance of Le mex=2690 106 vhenrys. Equation ,10c will lshow that, in order to obtain an inductance of 1500/2690:0.j56 times as much as the 8-layer inductance, while atthe same time having a somewhat smaller coil-radius A53 anda smaller coil-thickness or radial depth T53, would require a turn-ratio, squared fied'in Equations 11f, the transformer-dimeny sions willbe asfollows: Y z

7' 'I of the per-formanee-characteristids listed .in Equations 11g, we now have, for jtheis'eq# ondary tap 43, z:

Ln* 0.8 X 1.2611- X 14,400X 10"s =1473 X l*a henrys v`0.9643 l mori-'7646? Fig. 10, plotted to the same scalo as Fig. 9, shows the operating-conditions for the transformer-tap 43. The circle 416s, having a diameter represents the input-impedance Zi of the network, in terms of the primary inductance wIm, at the minimum tap 43 frequency, fs m1n=65 kilocycles. "Atany other tap S'frequency, f3, the diameter of the new circle 4|3, corresponding to the circle represents the `apparent cable-impedance ZB, in

terms of the primary inductance wLp, at the minimum tap-43 frequency, f3 m1n=65 kilocycles,

`assuming the same voltage-ratio, b=0.5142, as in 'Fig 9. lit any other tap-3 frequency, f3, still assuming the same voltage-ratio, b=0.5142, the center-displacement becomes and the circle-radius becomes the vcenter-displacement. Ros of TABLE In (For Fig. 1o)

Q. z c5: Rm XF: Roi P1 Ru pa l 000 9219 +1329' 8718 1. 2090 1. 471 1i 345 1.100 65, 000 9987 121.' 99 1. 0235 1. 358 1. 069 1. 104 75, 000 1.1523 1958' 1. 0180 6302 1.177 050 1 057 90, 000 1. 3828 40""53l 7884 3154 9805 369 7975 105, 000 1. 0133 52`18y 5897 2231 v 840 335 084 000 1. 8437 50"59 1614 2014 735 340 v. 598 135, 000 2. 0742 6446' 3770 2001 054 .342 532 150, 000 2. 3047 -68110' 31845 20435 588 336 '.4785 105, 000 2,5351 7043r i. 2705 l2098 535 332 435 Rc=50, Rl.=*450, C=.004X10"G, L|=1473X10', Lp=155X10',

k=.se4, f=.514.

'I'he last two columns of Table III show that PBR/o3 is less than 42's, and hence the standingwave voltage-ratio Es/Epzb is less than the assumed value 0.5151, throughout the frequencyrange starting slightly below 65 klocycles and ending considerably above 165 kilocycles.

Thus, it is possible, using only one intermediate secondary tap 43 in addition `to the full-turn secondary terminal 24, to couple any carrierfrequency from l5 to 165 kilocycles, and more, without introducing a reflected wave En any larger. than 0.514 times the forward Wave Er, and without encountering va loss of more than 1.54 db in the coupling-cable TLo.

In Fig. 10, one additional pair of circles 4h05 and 41105, are drawn,.by way of illustration, for a frequency of kilocycles, in addition to the initial circles Ms and42s5 forthe minimum frequency, 65'kilocycles, for this tap 43.

One moreexample will suilice, and only the beginnings of the calculation of this second example of coupling-transformer I4 will need to be indicated.

Instead of assuming one of 'the largest coupling-capacitors, C, which is likely to be encountered inpractice, as was done in Equation 11, where C was 0.004 microfarad, let us assume one of the smallest likely couplingcapacitors, where the other line-constants being as stated in Equation' 11 (not including the coupling-coefficient f as a line-constant).

lAlso, by way of example, let us now assume a two-winding coupling-transformer, instead of the single-winding transformer or autotransformer which, was shown in Fig. 8.

It is not necessary that the minimum frequency of the carrier-current frequency-band vshall be at the extremeflower edge of the frequency-band which is served by the maximum secondary inductance L: maas previously assumed. For example, the lowest carrier-frevery roughly, whence the maximum secondary inductancer is Ialfosmfllooxm henrys, roughly.y

=tan*1(6.0467.226):tan-1(-1.l80)=4943 This two-winding transformer would normally (or frequently) be made with heavier Wire for the primary. It is also evident, from Equation 13a, that it ywill have many more turns than the transformer` of my iirst illustration. Both of these factors contribute to maketliis two- Winding Vtransformer -have a- --much smaller coupling-coecient, which can be initially estimated at 1c4:'0.46, or m2202116, for a first'z gllSS. Hencethe Fig. 4 circle-diameter shouldj be (1164) k I 2 6 vvc8274 i15m i minLM-O.- y Rr o 1-53.0

roughly.

The cofordinates oi the operating-point 1?4- should be inizi-1.53 dos 4943' sin leusizlzflszvbto roughly.

If (for example) we desire a rather low loss of 1.2' decibels at Athis minimum frequency'in thecable TLc, 'he`poWer-ratio Pi/'Puzanniog 0,12=1.318

and hence thestanding-'wave voltage-ratio EB/EF (-869 mism-1137336 approximately, and the center-displacement r of the Fig. 7 circle representing the apparent cableimpedance Za in' terms of the characteristic cable-impedanceRewillbe 1+0.11 3 Q i I)" `i-o.1131255-4 V1-575 approximately-.5 Hence,`

various ways. In a tWowindingaircore design of the type shown in Fig; 8,` .counting the inside coil Lp, in Fig. yasthe primary winding which is to have the desired inductance Lpl, and

counting the outside coil L2, inv Fig; 8, as the secondary winding which is to have thev desired in ductance L54, we can obtain a` preliminary idea of the relative proportions, orthegeneral shape,

the primary inductance 26' which will be needed, by using the following formula for the approximate value of thecoupling-coecient R24, as given in Termans Formula 87 on page 71:

where a4 and A4 are the mean radii of the inner and outer coils, respectively, and :mand X4 are the, axial lengths of the respective coils. Thus.

the ratio of the two radii will be (1312 n- En #Jn A -\/k4 x4 .46 x4 x4 Thus, ior example,l if the outer coil has a. length of approximately X4=1.2 inc hes. and the inner coil has a length of approximately :c4=1.1-

inches, and if the inner coil has a mean radius of approximately a4=1.12 inchesthe outer coil will have a mean radius of approximately (13C) 1.12 Q f A4-0 678 1 2l.58 inches portions which will be required. U A

Several trials may vbe necessary, in order to nnd a transformer,approximatingthe required constants, although only a roughk approximation is necessary, as the losses do not vary too rapidly with changes in the transformer-constants. and we will provide a suflicient (but small) number of secondary `t`aps"(such as the tap 43) so that we can choose whichever tap whichmay give which gives a rough deaof the'generai protheV best available joperatingconditions for any assigned. frequency.- Y

To give one example, we 'm'ay choose a two-coil transformer-design, wound on a mandrel V39 (Fig. 8) having a radiusof 1.0105finches, andaprimary winding orv inner coil', corresponding toA thev coil Liq in Fig. 8, which is'wound in'3flayers 40(Fig. 8)', each layer'containingv 16. turns 4of No. 15 doc. enameled Wire, which We will assume to. have a b arewire-diameter of .057. inch, pluswire-insulation'INSw'having a thickness 'of .0055 inch,

making an outside wire-diameter"of} .068 inch.

Let us choo'sea"secondarywindingv or outer coil. corresponding to'thefcoil L2 'in Llig. 8, which is woundin 1 4 layersdll'ilig. 8),- each'layercom taining 28 turns fof. No. 20 dcc. 1enameled wire."-

v vhich we will` assume to have a barey wire-di-y ameter of ..032 inch, plus wire-insulation IN/Sw having/a.l thickness of .0055 inch,y making an outside wire-diameter vof .043 inch. f Then, i1 sheet-insulation INSS having a thickness of .005 inch is. used between successive layers of both theV primary andV the secondary Windings, as shown in Fig. 8,v we will have the following transformer-'dimensions and characteristics:

7 X .043 +9.5 X .005 :1.563 inches :x 1705 henrys It is to be noted that whereas we started out withl a tentativeassumption'vof a fairly high super-resonance conditionO in whichthe second-- ary reactance 101111111154 was 1.2 times the couplingcapacitor 'reactance-1-/wmm6'4, at the minimum frequency, our actual design produced a secondand1 our actual minimum-'frequency operating? Y angley turned out to be '4=-`74548 insteadof the initially assumed value ofj41 --4943." Our decibel-lo'ss-jin the cable, howeveryturnedoutto be log P1/F5: 1..2,which isjprecisely what was originally as sumedf Qur'actual secondary inductan'ce'L'n turned out-'tobe' atriflelower thanth initially assumedv value, in .the ratio 11,260 to 11,500; and our actualprimary 'inductance Lm tuned out-jte be still. lower than theV initially assumed value, in the ratio 125 to 145. .Our initially assumedA value of the coupling-coeilcient,v kif-40.416; proved to be quite adequately closeto theactual yalue, whichwas 1c4=n0.4.61'5. l

' -To determine the range Aof frequencies over. which thistwo-winding transformer of Equationsv 130iA is'operativeg withreasonable values of the, decibel-loss, 'instead of assuming that the stand- -l ing-wave voltage-ratio b (and hence the decibelloss) remainsjconstant, vand increasing' theisiz'e ofv the unmatclled-coupling circle 42, in inverse ratio to the frequency, as in Figs. 9 and 10`for theV autotransformer, (so as to determine whether the operating-point P, for each frequency, Vfalls in. side of the unmatched-coupling circle. 4,2"fo1- that frequency), I will now illustrate a different manner in which the performance, at different frequencies, can be estimated, namely, byfactually calculating the voltage-ratio 174x for each of a number of frequencies other than the minimum frequency of 45 kilocycles for which the original design was made. Thus, for each frequency f4x, we can successively calculate the input-impedance ende-diameter ikiwara/RL, the

angle e414 from Equation 4b, the co-ordinates1 28` Table IV shows the results of such a calculation, for theimaximum-turn secondary-tap 24 of the two-winding transformer which is dened in Equations 13d, starting out with different assumed values of the frequency f4x.

TABLE IV Two-winding transformer fix i Q04: i 474x Rmx l X94: R041 b4: (1b-10551 30,000 1.300 +4012 0.702 1.044 2.391 .040 1.00 41,000 1.373 +1049 1.325 1.253 1.304 .400 1.31 43,000 v1.440 -2325' 1.213 .475 1.082 .10s 1.07Y 45,000 1. 507 -454s' 0.733 i .247 1.255 .335 1.20 I 47,000 1.574 5520l .442 .293 1.707 .520 1.575 40,000 1. 541 05 4l .202 .373 2.520 .057 2. 0s 51,000 1.708 -e03a' .2085| .441 3.440 .742 2.02 ,000 1.775 723a' .15s I .404 4.500 I .70s 3.17

Table IV shows that the maximum number of secondary turns on the two-winding transformer defined in Equations 13d suffices for a band of frequencies extending from well below 39 kilocycles (kc.) to 53 kilocycles (kc.), with losses which are always below 3.2 db in the cable TLc; or if the band is extended up to only 49 kc., the cable-losses are always below 2.1 db.

Without going through the calculations for the additional secondary taps (such as 43) which are necessary to couple carrier-currents of higher frequencies to the coupling-capacitor C4 and thence to the power-line TLr., it will sufhce to say that four additional secondary taps, at the ends kc., the six-layer, 16S-turn tap wllhandle this frequency with a cable-loss which isprobably less'than 3.2 db, or another tap may be provided, with still fewer secondary turns, to provide still lower cable-losses.

In all of these discussions of decibel-losses in f the connecting-cable TLc, I am assuming a cable which would have a loss of exactly 1 decibel with perfectly matched coupling-impedances at the least advantageous (that is, usually the highest) frequency, and at the least advantageous (that is, the highest) value of the power-line impulseimpedance R1.. Actually, the loss varies with the frequency, and with the length and the other design-constants of the cable, so that, in general, the losses will be less than the figures given, although occasionally the losses may approach, or even exceed, these figures. l

It will be noted that my two-winding transformer-design is an example of a design in which I have chosen the smaller of the two calculated primary-inductances corresponding to anyy desired standing-wave voltage-ratio b. In other words, I have chosenA the negative sign in front ofthe radicalin Equations 9h and 9h4, illustrative autotransformer design, which was considered in my. rst exemplary design-calcu- 1ation,.I chose', by way of example, the larger primary inductance, -thatfis, the positive sign before vthe radical in Equations 9h and 11e.

. From the foregoing mathematical and theoreti- In my cal discussions, it will bev evident that a 'distinc-z tive feature of my present invention is that thel coupling-transformer I4` is knot necessarilyldeliberately designed to'produce matched-couplingv conditions at any frequency. An important'feafi ture of my design is that any given Ysecondary inductance Ls, such as is provided by any oneof.

the secondary taps or terminals, 24 or 43, is usable over a range of frequencies such that, at the..ex.

treme upper or lower frequencies of thisV range,v are vdefinitely mis`v backward wave-EB.

the coupling-conditions matched so that a reflected or is produced.

Consequently, the decibel-.losses inV the pling-cable 'I'Le are necessarily higher than 'the decibel-losses which would have been. encountered under matched-impedance conditionsr.' Itv is in this'way thatI am enabled to use a single or specific value of` secondary inductance Lex over amaterial width or range of carrier-.current frequencies, so that `only a relatively small number of secondarytaps 24 and 43y will suce tofcover the entire range of carrier-current frequencies without introducingva prohibitively high4 decibel-loss inthev coupling-apparatus.'v 1 .Reference to Table IV will show,.. for example,

that 'a particular value of secondary inductance'. suclras Ier, will operate over a frequency. range between 39r and 49 kilocycles while the.

standing-wave voltage-ratio bvaries from6`4 dovvnl to .2- or less, and up to .66 again', vover this frequency-range, while the cable-loss variesv from 2.0 decibels downto 1.1 decibels or less, and up to 2.1 decibels, over this same frequency-range, assuming that thecable-lossv would have been 1.0 decibel under exactly matched-impedance conditions. extended to includev 53 kilocycles,l the standing- Wave voltage-ratio b wouldihave'reached .8, 'and the .cable-loss would haveV reached 3.2. decibels. The exactwidth of .the frequency-band which is served by any one secondary tap of the transformer .depends upon the maximum decibel-'loss which is tobe accepted in the lead-in vcable TLo. .In order that? this frequency-band may have. any material width.. it is necessaryA to accept a certain .amount of.` decibel-loss, or a certain standing-wavev voltage-ratio b, at the extremeV end'or ends vof, the acceptable frequencyband, and hence the coupling-transformer I4'l overlapping frequency-ranges which are ,applicable to adjacent secondary taps, and `much higher values are frequently found to bequite acceptable, for instance,` a voltage-ratio b as high as 0.8, .or even. slightly higher, and a decibel-loss of 3.2, oreven slightly higher;

My coupling-transformer lI4 is novel also, in the manner of its design, or in the correlation between the primary inductance Lp, the secondaryinductance Ls, and the coupling-coeflicient k of the rcoupling-transformer, and the characteristie impedances, Reand Rr. ofthe .two communi- If 'this :frequency-band had been spectively. t

cation-circuit transmission lines 'ILC and Tx.. ref-f `It is anV important feature of l my invention.

as hereinabove described, that the secondarycircuit reactance (wLs-l/we) shall be some.-

where near resonancev (within the limits .indi-' cated) at the minimum frequency of the range of Vfrequencies over which that particular' value. of A`secondary inductance Ls is to be usable.'

It is a feature of .my invention that theFig. circle-diameter QG=k2wLs/RL shall not be Asmall,witl`1 relation to unityfto produce `a rea'fll sonablev ratio of secondary-to-primary inductances', Ls/Lp, while at the same time providing a reasonable range of acceptable frequencies. as' theoperating-point P travels clockwise'around a vlocus of the type shown at =Prin Fig: 9*,iwith"V increasing values of the frequency.

It is another important feature of my invention to use the primary inductanceL'p' so that it; is correlated with the value of thecharacteri'stic impedanceRe of the lead-in cable TLc,` sothat" the value of this impedance-is fitted to accom? modate the value of the `power-line characteristicimpedance RL, or to accommodate' the varying" value of the Fig. 4 circle-diameter -G, asA-the frequencyf, or the angular Velocity w=21rf, is

varied betvveenthe lower and upper -linn'ts of thej frequency-range' which is to be served -byfajn'y' given secondary tap. I

These and other novelfeatures of my' couplingtransfo'rme'r I4 are described and illustrated ini the foregoing specification. y

While,v as a matter' of convenience.` I 'use .the

term primary winding to refer'toA the'side of the transformer I4 Awhich is connected '-to`ftheshort transmission-line'or lead-in cable:'TI.sc.`fh and the term secondary Winding "to referItol the side of the transformer` I4 whichis iconnected to the capacitor C and thence to the long transmission-line or power-line TLL, this usage` of terms is not intended to imply vthatlthe direction of communication-circuit power-flow is solely from the short line to the long line; as the communication-network is' completely reversible.

as to the direction of current-flow.l `In fact, the

carrier-set E which is connected to the otherv end` of the short line TLc is illustrated as beingboth a transmitter for transmitting carrier-current energy to the long line vTLL, anda receiver. for

receiving.carrier-current energy which is transmitted from a similar carrier-set (notshowniat the far end ofthe long" line. Y l

Furthermore while, as a matter of I refer to the transformer ,I4 as having vprimary and secondary windings I use this; terminology in a sense applicable to an auto transformer as well as a two-winding. transformer.v j i It will be noted that I have made no effort to achieve the optimum possible design, that is, the best possible relation. between the threetr ans former-constants, which arev the primary inductance Lp, the secondary inductance Laand,v the coupling-coeicient lc. In general', the decibel-losses arey sufficiently low so that it is lnotat all necessary to go to the time and expense necessary. to find the absolute optimum .design-constants.- The solution involves trigonometric'and logarithmic functions which are practicallysolvable only by the laborious method of cut and try. and plotting the resultsk for any trends which can.

be observed, taking care lest one be misled by a tricky reversal of a trend, which may frequently occur with such complicated relationships. eral1examples of practical approaches to a design-calculation have been given. which are sutilcient to enable anyone skilled in the artto practicefmyinvention, whether the designer. wishes to content himself withtlie rst reasonably acceptable design which he achieves, or whether he wishes to Workout vany given number of designs.. so that he can pick out the best one of the bunch. An extremely important novel feature-of my transformer is that. it can now be -deiined. in terms of reasonable design-equations and designpx'ocedures, which is more than was ever possible, prior to my presentinvention, in a transformer designed forY mismatched-impedancev coupling.

, While I have given several concrete illustrations of myinvention, and while I have given certain concrete suggestions in regard to designformulasand design-procedures. I wishit to be understood that my-invention is not limited to all oi thesedetails. as-various departures will suggest themselves to those skilled in the art, possibly in addition to the variations which have already been suggested in this specification. I desire. thereforathat the appended claims shall be accorded the broadest construction consistent with their language. v

"I claim as my invention: A

, 1. A novel coupling-transiormerv ladapted. to couple. a` carrier-frequency lead-in communica.- tion-line cable. having alength which is considerably less than one wavelength of the carrier' wavetoa serially connected coupling-transformer and thence to a carrierfrequency communications-transmitting line whichA is very long as compared tothe wavelength of the carrier wave! .said coupling-transformer being*` characterized by having apredetermined value of primary inductance. apredetermined value of secondary inductance, and. .a predetermined value of couplingcoefficient which are .usable over a material. range of carrier frequencies. the upper and lower limits of` said usable frequency-range. v producing. mismatched-impedance coupling-conditions :in which the backward-to-forward standing-wave voltage-ratio is of the order of 0.5` or' more in said cable,V said voltage-ratiov being lower at intermediete-frequencies than at. said upperand lower frequency-limits; the minimum-frequency back.-

ward-to-forwardl standing-wave voltage-ratio .iny

the cable bei-ng between the values oi approximately0i5 and approximately 0.'.8; f

`2. 'Ihe'invention as.v denedin claim` l, charac;- terized by the transformer-constants being. such` as to provide mismatched-impedance: coupling at.'

all frequencies.

3'. A.- novel coupling-transformer adapted to: couple acarrier-frequency.lead-in commmcation-line cable, having a lengtlr which is considerably less than one wavelength? ofthe. carrier wave, to a' serially connected coupling-transformer and' thence toa carrier-frequency conrmunications-transmitting line which very long` as. 'compared tothe wavelength of' the'Y carrier' wave, said coupling-transformer being charac.- terized'` by having a predetermined Avalue. ot .prilmary. inductance, a predeterminedavalue ot sec-iondaryl inductance, and. a predetermined: value. oi" coupling-coeiilci'ent.which. are usable over a; material intermediate rangepof carrier frequenciesg. lesseA than the aforesaid-predetermined range-.fot frequencies., the; upper'. and; lower of saidfv usable. intermediate. frequency-range producing mismatched-impedance coupling-conditions.

which: the; backward-to-forward vstanding-wave voltage-rating is of the order. on 0:5 or .more in'said; cable,4 saidA voltage-ratio; being: lower'y at intermeprovide acceptable coupling-conditions over the.

aforesaid predetermined range of frequencies.

4. A novel coupling-transformer adapted to couple a carrier-frequency lead-in communication-line cable, having a length which is consid- I erably less than one wavelength of the carrier Wave, to a serially connected coupling-transformer and thence to a carrier-frequency communications-transmitting line which is very long as compared to the wavelength of the carrier wave, said coupling-transformer being characterized by having a predetermined value oi.' primary inductance, `a. predetermined value .of secondary inductance, and a predetermined value of coupling-coeflicient which are usable over a material range of carrier frequencies, the lower limit. of said usable frequency-range producing coupling-conditions in which the numerical value of the secondary-winding reactance, divided by the numerical value of the capacitor-reactance, is within the limits of approximately 110.2.

. 5. A novel coupling-transformer adapted to couple a carrier-frequency lead-in communica-- tion-line cable. having a length which is considerably less than one wavelength` of the jcarrier wave. to a serially connected coupling-transformer and` thence to a carrier-frequency cornmunications-transxnitting line which is very long as compared to .the wavelength of the carrier wave, said coupling-transformer having a relatively small number of secondary taps, any one of which may be used for a predetermined range of; carrier-frequenciesr said .coupling-transformer being characterized byl having a predetermined value' of primary inductance, a .maximum-turn value of secondary inductance. and a predetermined value of coupling-coeiicient which. are usable over a material Afirst intermediate range of carrier frequencies, said iirst intermediate range starting withv the lower limit of' the entire range of communication-circuit frequencies over adapt. the coupling-network to both the characteristic matched-coupling impedance and the mismatched-coupling apparent impedance ot said short transmission-line, the ratio of said` mismatched-coupling apparentv impedance. di'.- vided by the. primary-winding reactance having a: magnitude corresponding. to a backward-toforward.standing-wave voltage-ratio of. the. order of 0;5 or' more in: sai-d: cable. the minimumfrequency backward-to-forward standing-wave Ivoltage-ratio ini the cable being' between the 

